Theorem biimpri

Description: Infer a converse implication from a logical equivalence. Inference associated with biimpr . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 16-Sep-2013)

	Ref	Expression
Hypothesis	biimpri.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	biimpri	$$⊢\psi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		biimpri.1	$$⊢\phi \leftrightarrow \psi$$
2	1	bicomi	$$⊢\psi \leftrightarrow \phi$$
3	2	biimpi	$$⊢\psi \to \phi$$